Question

find three consecutive even integers for which -4 times the sum of the first and third is 192

Answer 1

Answer:

1. -26
2. -24
3. -22

Step-by-step explanation:

Let x be the smallest number (first)

Let (x + 2) be the second number (second)

Let (x + 4) be the greatest number (third)

Set equation according to the given information

-4 [x + (x + 4)] = 192

Simplify parentheses

-4 [x + x + 4] = 192

-4 [2x + 4] = 192

Expand bracket and apply the distributive property

(-4) · 2x + (-4) · 4 = 192

-8x - 16 = 192

Add 16 on both sides

-8x - 16 + 16 = 192 + 16

-8x = 208

Divide -8 on both sides

-8x / -8 = 208 / (-8)

$\boxed{x=-26}$

Find the value of the second term

x + 2 = (-26) + 2 = $\boxed{-24}$

Find the value of the third term

x + 4 = (-26) + 4 = $\boxed{-22}$

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